unit 8 - limits and rates of change

quick review:

this equationis really just  (equation at point 1) - (equation at point 2) all over  change in time (point 1-2)

so basically points 1&2 are numbers that are plugged into the variable(s) in the equation. (numerator)
then you find the difference between points 1&2... and this is your denominator


instantaneous rate of change - just make point 2, 0.1 or 0.01 greater than point 1.

average rate of change - the two points should be given.



limits.. is hard to explain.. lol..

lim                some equation/(x+h) - x
h->0  

lim                       some equation/h
h->0

lim                        simplify equation until you can cancel out the h in the denominator.
h->0

then plug in h as zero.

there's your general slope of the tangent to the equation.

to find the equation of the tangent to the equation,

plug in the given coordinates into y = mx+b, with m as the general slope you found earlier.

find b

then rewrite the equation without the points

y = mx+b    plug in m and b values!

tada!